Absolutely Stable Time Domain Integral Equation Methods in Computational Electromagnetism

University Of Delaware, Newark DE

Investigators

Abstract

Despite decades of advances in computational electromagnetics (CEM), some problems still elude efficient and accurate solutions. Problems occurring in the analysis of microelectromechanial systems, electromagnetic compatibility, and ultra wide band antenna design involve complex geometry, small structures, and large propagation distances across homogeneous regions. Solutions to problems with these characteristics are most efficiently computed (in principle) by time-domain integral equation (TDIE) techniques. Unfortunately, while TDIEs have been researched for more than thirty years, there is still no TDIE scheme for CEM that can efficiently model curvilinear geometry while ensuring stability. Thus, current techniques are either of low order of convergence or unreliable stability. Mathematical error analysis, work estimates and computer programs created under this proposal will demonstrate a new method, based on convolution quadrature, that promises to deliver both superlinear accuracy and unconditional stability. Electromagnetic theory governs the behavior of light, radio waves, and microwaves. Understanding the behavior of electromagnetic waves is of the utmost concern to national security (in the design of radar and surveillance systems and protecting them from interference), energy systems (in the collection and distribution of electric power), and the economy (in cell phones and television broadcasts). Unfortunately, as electromagnetic systems become more complicated and powerful, they become harder to simulate and therefore design. For instance, modern problems in shielding devices from electromagnetic interference involve broad bandwidths, long propagation distances, and small features. While it has been known for decades that this combination of difficulties can be mitigated using time domain integral equation formulations, no such formulation has been produced that can accurately model arbitrary geometry without producing a solution with exponentially increasing error. This proposal produces such a scheme by introducing a new method for modeling the time dependence of the solution.